The low-temperature behavior of the static magnetic susceptibility $\ensuremath{\chi}(T)$ of exchange-disordered antiferromagnetic spin chains is investigated. It is shown that for a relatively small and even number of spins in the chain, two exchange distributions which are expected to occur in nanochains of $P$ donors in silicon lead to qualitatively distinct behaviors of the low-temperature susceptibility. As a consequence, magnetic measurements might be useful to characterize whether a given sample meets the requirements compatible with Kane's original proposal for the exchange gates in a silicon-based quantum computer hardware. We also explore the dependence of $\ensuremath{\chi}(T)$ on the number of spins in the chain as it increases towards the thermodynamic limit, where any degree or distribution of disorder leads to the same low-temperature scaling behavior. We identify a crossover regime where the two distributions of disorder may not be clearly differentiated, but the characteristic scaling of the thermodynamic limit has not yet been reached.The low-temperature behavior of the static magnetic susceptibility $\ensuremath{\chi}(T)$ of exchange-disordered antiferromagnetic spin chains is investigated. It is shown that for a relatively small and even number of spins in the chain, two exchange distributions which are expected to occur in nanochains of $P$ donors in silicon lead to qualitatively distinct behaviors of the low-temperature susceptibility. As a consequence, magnetic measurements might be useful to characterize whether a given sample meets the requirements compatible with Kane's original proposal for the exchange gates in a silicon-based quantum computer hardware. We also explore the dependence of $\ensuremath{\chi}(T)$ on the number of spins in the chain as it increases towards the thermodynamic limit, where any degree or distribution of disorder leads to the same low-temperature scaling behavior. We identify a crossover regime where the two distributions of disorder may not be clearly differentiated, but the characteristic scaling of the thermodynamic limit has not yet been reached.

arXiv:cond-mat/0507246Physical Review BMar 10, 20063 citations

Entanglement between random and clean quantum spin chains

Róbert Juhász, István A. Kovács, Gergő Roósz +1 more

The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean and a random part, both being critical. In the composite, antiferromagnetic XX-chain with a sharp interface, the entropy is found to grow in a double-logarithmic fashion ${\cal S}\sim \ln\ln(L)$ , where $L$ is the length of the chain. We have also considered an extended defect at the interface, where the disorder penetrates into the homogeneous region in such a way that the strength of disorder decays with the distance $l$ from the contact point as $\sim l^{-\kappa}$ . For $\kappa<1/2$ , the entropy scales as ${\cal S}(\kappa) \simeq (1-2\kappa){\cal S}(\kappa=0)$ , while for $\kappa \ge 1/2$ , when the extended interface defect is an irrelevant perturbation, we recover the double-logarithmic scaling. These results are explained through strong-disorder RG arguments.The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean and a random part, both being critical. In the composite, antiferromagnetic XX-chain with a sharp interface, the entropy is found to grow in a double-logarithmic fashion ${\cal S}\sim \ln\ln(L)$, where $L$ is the length of the chain. We have also considered an extended defect at the interface, where the disorder penetrates into the homogeneous region in such a way that the strength of disorder decays with the distance $l$ from the contact point as $\sim l^{-\kappa}$. For $\kappa<1/2$, the entropy scales as ${\cal S}(\kappa) \simeq (1-2\kappa){\cal S}(\kappa=0)$, while for $\kappa \ge 1/2$, when the extended interface defect is an irrelevant perturbation, we recover the double-logarithmic scaling. These results are explained through strong-disorder RG arguments.

Jan 1, 20172 citations

Quantum disordered phase in a doped antiferromagnet

C. K�bert, A. Muramatsu

Journal of Low Temperature PhysicsMay 1, 19950 citations

Scaling of entanglement entropy at quantum critical points in random spin chains

Prashant Kumar, R. N. Bhatt

We study the scaling properties of entanglement entropy (EE) near the quantum critical points in interacting random antiferromagnetic (AFM) spin chains. Using density-matrix renormalization group, we compute the half-chain EE near the topological phase transition between the Haldane and random singlet phases in a disordered spin-1 chain. It is found to diverge logarithmically in system size with an effective central charge ${c}_{\mathrm{eff}}=1.17(4)$ at the quantum critical point (QCP). Moreover, a scaling analysis of EE yields the correlation length exponent $\ensuremath{\nu}=2.28(5)$. Our unbiased calculation establishes that the QCP is in the universality class of the infinite-randomness fixed point predicted by previous studies based on the strong disorder renormalization group technique. However, in the disordered spin-1/2 Majumdar-Ghosh chain, where a valence bond solid phase is unstable to disorder, the crossover length exponent obtained from a scaling analysis of EE disagrees with the expectation based on the Imry-Ma argument. We provide a possible explanation.We study the scaling properties of entanglement entropy (EE) near the quantum critical points in interacting random antiferromagnetic (AFM) spin chains. Using density-matrix renormalization group, we compute the half-chain EE near the topological phase transition between the Haldane and random singlet phases in a disordered spin-1 chain. It is found to diverge logarithmically in system size with an effective central charge ${c}_{\mathrm{eff}}=1.17(4)$ at the quantum critical point (QCP). Moreover, a scaling analysis of EE yields the correlation length exponent $\ensuremath{\nu}=2.28(5)$. Our unbiased calculation establishes that the QCP is in the universality class of the infinite-randomness fixed point predicted by previous studies based on the strong disorder renormalization group technique. However, in the disordered spin-1/2 Majumdar-Ghosh chain, where a valence bond solid phase is unstable to disorder, the crossover length exponent obtained from a scaling analysis of EE disagrees with the expectation based on the Imry-Ma argument. We provide a possible explanation.

arXiv:2307.00062Physical review. B./Physical review. BDec 15, 20232 citations

Quantum disordered phase in an antiferromagnet via doping

C. Kübert, A. Muramatsu

arXiv:cond-mat/9407112Physica C SuperconductivityDec 1, 19940 citations

P

donors in silicon lead to qualitatively distinct behaviors of the low-temperature susceptibility. As a consequence, magnetic measurements might be useful to characterize whether a given sample meets the requirements compatible with Kane's original proposal for the exchange gates in a silicon-based quantum computer hardware. We also explore the dependence of $\ensuremath{\chi}(T)$ on the number of spins in the chain as it increases towards the thermodynamic limit, where any degree or distribution of disorder leads to the same low-temperature scaling behavior. We identify a crossover regime where the two distributions of disorder may not be clearly differentiated, but the characteristic scaling of the thermodynamic limit has not yet been reached.

{\cal S}\sim \ln\ln(L)

, where

L

is the length of the chain. We have also considered an extended defect at the interface, where the disorder penetrates into the homogeneous region in such a way that the strength of disorder decays with the distance

l

from the contact point as

\sim l^{-\kappa}

. For

\kappa<1/2

, the entropy scales as

{\cal S}(\kappa) \simeq (1-2\kappa){\cal S}(\kappa=0)

, while for

\kappa \ge 1/2

, when the extended interface defect is an irrelevant perturbation, we recover the double-logarithmic scaling. These results are explained through strong-disorder RG arguments.

{c}_{\mathrm{eff}}=1.17(4)

at the quantum critical point (QCP). Moreover, a scaling analysis of EE yields the correlation length exponent $\ensuremath{\nu}=2.28(5)$. Our unbiased calculation establishes that the QCP is in the universality class of the infinite-randomness fixed point predicted by previous studies based on the strong disorder renormalization group technique. However, in the disordered spin-1/2 Majumdar-Ghosh chain, where a valence bond solid phase is unstable to disorder, the crossover length exponent obtained from a scaling analysis of EE disagrees with the expectation based on the Imry-Ma argument. We provide a possible explanation.